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 A250438 Number of (n+1)X(3+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column 1

%I #4 Nov 22 2014 22:21:57

%S 1296,14400,160000,1000000,6250000,27562500,121550625,423536400,

%T 1475789056,4337012736,12745506816,32920473600,85030560000,

%U 198470250000,463250390625,996503062500,2143588810000,4311270849600,8670998958336

%N Number of (n+1)X(3+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column

%C Column 3 of A250443

%H R. H. Hardin, <a href="/A250438/b250438.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +14*a(n-2) -30*a(n-3) -90*a(n-4) +210*a(n-5) +350*a(n-6) -910*a(n-7) -910*a(n-8) +2730*a(n-9) +1638*a(n-10) -6006*a(n-11) -2002*a(n-12) +10010*a(n-13) +1430*a(n-14) -12870*a(n-15) +12870*a(n-17) -1430*a(n-18) -10010*a(n-19) +2002*a(n-20) +6006*a(n-21) -1638*a(n-22) -2730*a(n-23) +910*a(n-24) +910*a(n-25) -350*a(n-26) -210*a(n-27) +90*a(n-28) +30*a(n-29) -14*a(n-30) -2*a(n-31) +a(n-32)

%F Empirical for n mod 2 = 0: a(n) = (1/1358954496)*n^16 + (5/84934656)*n^15 + (31/14155776)*n^14 + (2135/42467328)*n^13 + (33847/42467328)*n^12 + (32735/3538944)*n^11 + (431429/5308416)*n^10 + (1463225/2654208)*n^9 + (5160755/1769472)*n^8 + (8008825/663552)*n^7 + (12913699/331776)*n^6 + (6965/72)*n^5 + (139417/768)*n^4 + (23855/96)*n^3 + (3741/16)*n^2 + 135*n + 36

%F Empirical for n mod 2 = 1: a(n) = (1/1358954496)*n^16 + (5/84934656)*n^15 + (373/169869312)*n^14 + (1435/28311552)*n^13 + (275299/339738624)*n^12 + (807985/84934656)*n^11 + (14409143/169869312)*n^10 + (49767325/84934656)*n^9 + (2153003003/679477248)*n^8 + (380990005/28311552)*n^7 + (7598369275/169869312)*n^6 + (9778683875/84934656)*n^5 + (76415846875/339738624)*n^4 + (9127365625/28311552)*n^3 + (2011296875/6291456)*n^2 + (616328125/3145728)*n + (937890625/16777216)

%e Some solutions for n=3

%e ..0..1..0..1....0..0..1..1....0..0..0..2....0..0..1..0....0..0..0..1

%e ..1..2..2..2....0..0..0..0....1..2..2..2....1..0..2..1....0..1..2..2

%e ..0..1..0..1....0..1..2..2....2..2..2..2....0..2..2..2....1..0..2..2

%e ..2..2..2..2....0..0..1..1....2..2..2..2....1..1..2..1....0..1..2..2

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2014

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Last modified August 3 08:07 EDT 2024. Contains 374885 sequences. (Running on oeis4.)